Some practical issues in the design and analysis of computer experiments

Deterministic computer simulations of physical experiments are now common techniques in science and engineering. Often, physical experiments are too time consuming, expensive or impossible to conduct. Complex computer models or codes, rather than physical experiments lead to the study of computer experiments, which are used to investigate many scientific phenomena of this nature. A computer experiment consists of a number of runs of the computer code with different input choices. The Design and Analysis of Computer Experiments is a rapidly growing technique in statistical experimental design. This thesis investigates some practical issues in the design and analysis of computer experiments and attempts to answer some of the questions faced by experimenters using computer experiments. In particular, the question of the number of computer experiments and how they should be augmented is studied and attention is given to when the response is a function over time.

Populations of models, experimental designs and coverage of parameter space by Latin Hypercube and Orthogonal Sampling

In this paper we have used simulations to make a conjecture about the coverage of a t-dimensional subspace of a d-dimensional parameter space of size n when performing k trials of Latin Hypercube sampling. This takes the form P(k,n,d,t) = 1 - e^(-k/n^(t-1)). We suggest that this coverage formula is independent of d and this allows us to make connections between building Populations of Models and Experimental Designs. We also show that Orthogonal sampling is superior to Latin Hypercube sampling in terms of allowing a more uniform coverage of the t-dimensional subspace at the sub-block size level. These ideas have particular relevance when attempting to perform uncertainty quantification and sensitivity analyses.

Sample size considerations and augmentation of computer experiments

Computer Experiments, consisting of a number of runs of a computer model with different inputs, are now common-place in scientific research. Using a simple fire model for illustration some guidelines are given for the size of a computer experiment. A graph is provided relating the error of prediction to the sample size which should be of use when designing computer experiments. Methods for augmenting computer experiments with extra runs are also described and illustrated. The simplest method involves adding one point at a time choosing that point with the maximum prediction variance. Another method that appears to work well is to choose points from a candidate set with maximum determinant of the variance covariance matrix of predictions.

Spatially stratified sampling using auxiliary information for geostatistical mapping

This paper presents a method of spatial sampling based on stratification by Local Moran’s I i calculated using auxiliary information. The sampling technique is compared to other design-based approaches including simple random sampling, systematic sampling on a regular grid, conditional Latin Hypercube sampling and stratified sampling based on auxiliary information, and is illustrated using two different spatial data sets. Each of the samples for the two data sets is interpolated using regression kriging to form a geostatistical map for their respective areas. The proposed technique is shown to be competitive in reproducing specific areas of interest with high accuracy.

Caffeine ingestion and cycling power output in a low or normal muscle glycogen state

Purpose Commencing selected workouts with low muscle glycogen availability augments several markers of training adaptation compared with undertaking the same sessions with normal glycogen content. However, low glycogen availability reduces the capacity to perform high-intensity (>85% of peak aerobic power (V·O2peak)) endurance exercise. We determined whether a low dose of caffeine could partially rescue the reduction in maximal self-selected power output observed when individuals commenced high-intensity interval training with low (LOW) compared with normal (NORM) glycogen availability. Methods Twelve endurance-trained cyclists/triathletes performed four experimental trials using a double-blind Latin square design. Muscle glycogen content was manipulated via exercise–diet interventions so that two experimental trials were commenced with LOW and two with NORM muscle glycogen availability. Sixty minutes before an experimental trial, subjects ingested a capsule containing anhydrous caffeine (CAFF, 3 mg-1·kg-1 body mass) or placebo (PLBO). Instantaneous power output was measured throughout high-intensity interval training (8 × 5-min bouts at maximum self-selected intensity with 1-min recovery). Results There were significant main effects for both preexercise glycogen content and caffeine ingestion on power output. LOW reduced power output by approximately 8% compared with NORM (P < 0.01), whereas caffeine increased power output by 2.8% and 3.5% for NORM and LOW, respectively, (P < 0.01). Conclusion We conclude that caffeine enhanced power output independently of muscle glycogen concentration but could not fully restore power output to levels commensurate with that when subjects commenced exercise with normal glycogen availability. However, the reported increase in power output does provide a likely performance benefit and may provide a means to further enhance the already augmented training response observed when selected sessions are commenced with reduced muscle glycogen availability. It has long been known that endurance training induces a multitude of metabolic and morphological adaptations that improve the resistance of the trained musculature to fatigue and enhance endurance capacity and/or exercise performance (13). Accumulating evidence now suggests that many of these adaptations can be modified by nutrient availability (9–11,21). Growing evidence suggests that training with reduced muscle glycogen using a “train twice every second day” compared with a more traditional “train once daily” approach can enhance the acute training response (29) and markers representative of endurance training adaptation after short-term (3–10 wk) training interventions (8,16,30). Of note is that the superior training adaptation in these previous studies was attained despite a reduction in maximal self-selected power output (16,30). The most obvious factor underlying the reduced intensity during a second training bout is the reduction in muscle glycogen availability. However, there is also the possibility that other metabolic and/or neural factors may be responsible for the power drop-off observed when two exercise bouts are performed in close proximity. Regardless of the precise mechanism(s), there remains the intriguing possibility that the magnitude of training adaptation previously reported in the face of a reduced training intensity (Hulston et al. (16) and Yeo et al.) might be further augmented, and/or other aspects of the training stimulus better preserved, if power output was not compromised. Caffeine ingestion is a possible strategy that might “rescue” the aforementioned reduction in power output that occurs when individuals commence high-intensity interval training (HIT) with low compared with normal glycogen availability. Recent evidence suggests that, at least in endurance-based events, the maximal benefits of caffeine are seen at small to moderate (2–3 mg·kg-1 body mass (BM)) doses (for reviews, see Refs. (3,24)). Accordingly, in this study, we aimed to determine the effect of a low dose of caffeine (3 mg·kg-1 BM) on maximal self-selected power output during HIT commenced with either normal (NORM) or low (LOW) muscle glycogen availability. We hypothesized that even under conditions of low glycogen availability, caffeine would increase maximal self-selected power output and thereby partially rescue the reduction in training intensity observed when individuals commence HIT with low glycogen availability.

Estimates on the coverage of parameter space using populations of models

In this paper we provide estimates for the coverage of parameter space when using Latin Hypercube Sampling, which forms the basis of building so-called populations of models. The estimates are obtained using combinatorial counting arguments to determine how many trials, k, are needed in order to obtain specified parameter space coverage for a given value of the discretisation size n. In the case of two dimensions, we show that if the ratio (Ø) of trials to discretisation size is greater than 1, then as n becomes moderately large the fractional coverage behaves as 1-exp-ø. We compare these estimates with simulation results obtained from an implementation of Latin Hypercube Sampling using MATLAB.

Sampling Methods for Exploring Between Subject Variability in Cardiac Electrophysiology Experiments

Between-subject and within-subject variability is ubiquitous in biology and physiology and understanding and dealing with this is one of the biggest challenges in medicine. At the same time it is difficult to investigate this variability by experiments alone. A recent modelling and simulation approach, known as population of models (POM), allows this exploration to take place by building a mathematical model consisting of multiple parameter sets calibrated against experimental data. However, finding such sets within a high-dimensional parameter space of complex electrophysiological models is computationally challenging. By placing the POM approach within a statistical framework, we develop a novel and efficient algorithm based on sequential Monte Carlo (SMC). We compare the SMC approach with Latin hypercube sampling (LHS), a method commonly adopted in the literature for obtaining the POM, in terms of efficiency and output variability in the presence of a drug block through an in-depth investigation via the Beeler-Reuter cardiac electrophysiological model. We show improved efficiency via SMC and that it produces similar responses to LHS when making out-of-sample predictions in the presence of a simulated drug block.

Probabilistic load flow for distribution systems with uncertain PV generation

Large integration of solar Photo Voltaic (PV) in distribution network has resulted in over-voltage problems. Several control techniques are developed to address over-voltage problem using Deterministic Load Flow (DLF). However, intermittent characteristics of PV generation require Probabilistic Load Flow (PLF) to introduce variability in analysis that is ignored in DLF. The traditional PLF techniques are not suitable for distribution systems and suffer from several drawbacks such as computational burden (Monte Carlo, Conventional convolution), sensitive accuracy with the complexity of system (point estimation method), requirement of necessary linearization (multi-linear simulation) and convergence problem (Gram–Charlier expansion, Cornish Fisher expansion). In this research, Latin Hypercube Sampling with Cholesky Decomposition (LHS-CD) is used to quantify the over-voltage issues with and without the voltage control algorithm in the distribution network with active generation. LHS technique is verified with a test network and real system from an Australian distribution network service provider. Accuracy and computational burden of simulated results are also compared with Monte Carlo simulations.

Design democratisation and its understandings through the meaning of the word “design” in Portuguese colonised countries

This paper explores the literature and analyses the different uses and understandings of the word “design” in Portuguese colonised countries, using Brazil as the main example. It investigates the relationship between the linguistic existence of terms to define and describe “design” as an activity and field, and the roles and perceptions of Design by the general society. It also addresses the effects that the lack of a proper translation causes on the local community from a cultural point of view. The current perception of Design in Portuguese colonies is associated to two main aspects: linguistic and historical. Both of them differentiate the countries taken into consideration from other countries that have a different background. The changes associated to the meaning of “design” throughout the years, caused a great impact on the perceptions that people have about Design. On the other hand, the development of Design has also influenced the changes on the meaning of the term, as a result of the legacy from the colonisation period and also as a characteristic of the Portuguese language. Design has developed and reached a level of excellence in Portuguese colonised countries that competes with the most traditional Design cultures in the world. However, this level of Design is enmeshed into an elite belonging to universities and specialised markets, therefore Design is not democratised. The ultimate aim of this study is to promote discussions on how to make the discourse surrounding this area more accessible to people from non-English speaking countries that do not have the word “design” in their local language.